(A U B)' = A' ∩ B': "not in either" = "not in A AND not in B". (A ∩ B)' = A' U B': "not in both" = "not in A OR not in B". These extend to any number of sets. Visualization: use Venn diagrams by shading each side independently and verifying they match. De Morgan's laws also apply to logical connectives.